Two-dimensional displacement discontinuity method for transversely isotropic materials

• Analysis of deformation of elastic body from force dipoles revisits and is explained in details.
• Relationships between force dipoles and displacement discontinuities are established.
• Displacement discontinuity method is outlined for transversely isotropic materials.
• Influence coefficients for one group of materials, missed in literature.
• The analysis is validated with analytical solution and finite element method.

This paper presents the fundamental solution for a two-dimensional displacement discontinuity method (DDM) for transversely isotropic elastic materials. We follow the procedures shown in the literature, in which there are some typographic errors and a lack of proper explanations for some expressions. Based on the fundamental solution of deformation due to a single point force in transversely isotropic materials, the formulation for deformation from force dipoles has been revisited. Generalised Hooke's Law is used to establish the relationship between dipole strengths and displacement discontinuities, which leads to the fundamental formulation of DDM for transversely isotropic materials. We present the full details of derivation and corrections to some expressions which have previously been presented with errors. In addition, we present the fundamental solution expressions for DDM for one situation which was not included in the literature. The fundamental solutions are implemented in an existing DDM code, FRACOD, and the method is verified by some examples with an analytic solution and finite element method. Furthermore an engineering application is simulated with the scheme.